That may be a big enough POD for a constitutional monarchy Russia, although personally I would have called the parliament the "Imperial Council", because council in Russian is "Soviet".
More seriously, I don't see how Britain can become socialist. If by socialist you mean social democratic, Labour is the route to that. If by socialist you mean revolutionary, I don't see how that's possible with a Russian POD. With a British one, that's possible, as FaBR has shown us, but not with a Russian one.
Well, Conservative Minister Pyotr Durnovo instituted a policy of forging alliances with Germany and the United States. When WWI came along, Russia chose Germany over France as an ally, and eventually pulled America in on the Central Powers side after a British ship sank the Lusitania.
With German industry, Russian manpower, and American war funds at their disposal, the Central Powers come out on top at the Treaty of Versailles, leading to the Allies (Britain, France, Austria-Hungary, and the Ottoman Empire) to become politically unstable.
France and Britain suffer massive inflation, the Ottomans fight a civil war, and Austria-Hungary splits into two nations. In Britain, the working classes are forced to suffer great poverty, while the upper classes, many of whom transferred their money to the American dollar to avoid the inflation, carried on as usual.
In 1918, a group of rioters near Westminster were shot at, and this news ignited a furor among the working classes. They became receptive to the ideas of the British Worker's Party, a fledgling group of left-wingers who had left the Labour Party and the Socialists in 1915, and advocated overthrowing the monarchy.
The following year, armed rebels took over major industrial cities, and many soldiers, having fought a war for aristocrats who seemed to not care about them, joined the revolution. A rump government was formed in Scotland, but that was soon crushed.
Britain officially went socialist in 1921, but it took several years to fully control the British Isles.
